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5 replies to this topic

### #1 HRAEDIUS

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Posted 29 February 2008 - 05:36 AM

find out what went wrong
the parts indented are just explaining what happened

a=b
2a=2b
2a(a-b)=2b(a-b)
2a(a-b)=2bxa-2bxb
(expansion)
2a(a-b)+a=2bxa-2bxb+a
(divide both sides except the "+a" by "a-b")
2a+a=2b-2b+a
2a+a=a
3a+a
3=1

Spoiler for spoiler

Edited by HRAEDIUS, 29 February 2008 - 05:43 AM.

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### #2 Mokirain

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Posted 29 February 2008 - 08:07 AM

Also, the last assumption is wrong:

3a=a (I'm pretty sure your + was a typo, since = is the logical operator for the problem and it wouldn't make sense otherwise) does not mean 3=1. a could equal 0, since 3x0=0.
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### #3 brhan

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Posted 29 February 2008 - 03:22 PM

a=b
2a=2b
2a(a-b)=2b(a-b)
2a(a-b)=2bxa-2bxb
(expansion)
2a(a-b)+a=2bxa-2bxb+a
(divide both sides except the "+a" by "a-b")
2a+a=2b-2b+a
2a+a=a
3a+a
3=1

Division by zero.
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### #4 wahledor

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Posted 29 February 2008 - 07:46 PM

find out what went wrong
the parts indented are just explaining what happened

a=b
2a=2b
2a(a-b)=2b(a-b)
2a(a-b)=2bxa-2bxb
(expansion)
2a(a-b)+a=2bxa-2bxb+a
(divide both sides except the "+a" by "a-b")
2a+a=2b-2b+a
2a+a=a
3a+a
3=1

In step 4 you expanded the right side but not the left side...

if you were to follow simple algebra rules and expand both sides of the equal sign the math would go a little different.

in step 4 we would have

2axa-2axb=2bxa-2bxb

now we continue with all other steps

2axa-2axb+a=2bxa-2bxb+a
now we divide by the zero even though that is incorrect. We are then left with
2a-2a+a=2b-2b+a
a=a
1=1
statement is true.
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### #5 brhan

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Posted 29 February 2008 - 08:27 PM

In step 4 you expanded the right side but not the left side...

if you were to follow simple algebra rules and expand both sides of the equal sign the math would go a little different.

in step 4 we would have

2axa-2axb=2bxa-2bxb

now we continue with all other steps

2axa-2axb+a=2bxa-2bxb+a
now we divide by the zero even though that is incorrect. We are then left with
2a-2a+a=2b-2b+a
a=a
1=1
statement is true.

According to the rules of algebra, expanding is legal.

It is always true that a(b-c)=ab-ac. This is always true irrespective of the values of a, b, and c.

Edited by brhan, 29 February 2008 - 08:27 PM.

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### #6 HRAEDIUS

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Posted 29 February 2008 - 09:09 PM

you got it (division by 0)

Edited by HRAEDIUS, 29 February 2008 - 09:09 PM.

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